Get source code from website and act like a browser to not get blocked (curl, file_get_contents, fopen)

Hello, I'm creating something similar to a proxy browser. For this I need to get the source code from websites. I tried this in PHP with curl, file_get_contents and fopen. This is working very well for many websites. But for some websites I'm asked to solve a Captcha or I'm getting a message like "failed to open stream: HTTP request failed! HTTP/1.1 403 Forbidden in - on line 12". When opening this website in a browser, there are no problems, although I'm using the same user agent and IP address as in my PHP script. This means, for the website I want to access, there is some difference between my PHP script and my browser. But, what is it? How can I make my PHP script act like my browser for the website I want to get the source code from? I need to get this work, no matter if you use curl, file_get_contents, fopen or anything else. I'll attach a file with my source code. I'll tell you a URL you can test it with via private chat. Who can do that for me?